{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "14ab30fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import matplotlib.patches as mpatches\n",
    "import pandas as pd\n",
    "\n",
    "y1 = np.arange(0.00,0.09,0.01)\n",
    "df1 = pd.read_csv(\"P_y_1m_1.csv\")\n",
    "P_Y_1 = np.loadtxt(\"P_y_1m_1.csv\", delimiter=\",\")\n",
    "P_Y_2 = np.loadtxt(\"P_y_2m_2.csv\", delimiter=\",\")\n",
    "#API Method for clay\n",
    "Gammades_s = 6.5\n",
    "Gamma1 = Gammades_s\n",
    "Cu = 35\n",
    "r_0 = 0.134\n",
    "z = 1\n",
    "D = 2*r_0\n",
    "X1 =z\n",
    "J = 0.5\n",
    "y_c = 2.5*0.01*2*r_0\n",
    "X_R = 6*D/((Gamma1*D/Cu)+J)\n",
    "if X1 <= X_R:\n",
    "    p_u = 3*Cu + Gamma1*X1 +J*Cu*X1/D\n",
    "else:\n",
    "    p_u = 9*Cu\n",
    "p_u\n",
    "API_y_1 = [0*y_c, 0.1*y_c, 0.3*y_c, 1*y_c, 3*y_c, 8*y_c, 0.25, .30 ]\n",
    "API_P1_1 = [0.00*p_u, 0.23*p_u, 0.33*p_u, 0.50*p_u, 0.72*p_u, p_u, p_u, p_u] \n",
    "\n",
    "z = 2\n",
    "D = 2*r_0\n",
    "X1 =z\n",
    "J = 0.5\n",
    "y_c = 2.5*0.01*2*r_0\n",
    "X_R = 6*D/((Gamma1*D/Cu)+J)\n",
    "if X1 <= X_R:\n",
    "    p_u = 3*Cu + Gamma1*X1 +J*Cu*X1/D\n",
    "else:\n",
    "    p_u = 9*Cu\n",
    "p_u\n",
    "API_y_2 = [0*y_c, 0.1*y_c, 0.3*y_c, 1*y_c, 3*y_c, 8*y_c, 0.25, .30 ]\n",
    "API_P1_2 = [0.00*p_u, 0.23*p_u, 0.33*p_u, 0.50*p_u, 0.72*p_u, p_u, p_u, p_u] \n",
    "Gong_x_2M = [0,0.0010611570139930323,0.002633943302589838,0.005249100728238606,0.008176593777464134,0.012669358764510048,0.01778924533048442,0.024785595969694298,0.0330361897667611,0.044627565905756984]\n",
    "Gong_y_2M = [0,16.43192488262912,23.161189358372454, 28.482003129890458, 33.020344287949925, 37.08920187793427, 41.94053208137714, 44.44444444444445, 48.5133020344288, 53.051643192488264]\n",
    "Gong_x_1M = [0,0.00042472417431987355,0.0015781770185016412,0.0037738376442837058,0.006698880361734318,0.012233689774928863,0.01787059634541184,0.02559616572083861,0.03436394287786568,0.046053005576955124,0.05972765379098998]\n",
    "Gong_y_1M = [0,6.729264475743349, 11.737089201877936, 15.179968701095461, 17.370892018779358, 19.718309859154928, 19.874804381846644, 20.97026604068857, 20.500782472613466, 18.622848200313, 18.935837245696405]\n",
    "\n",
    "plt.plot(y1,P_Y_1[:,300],linestyle='--',linewidth=2.5,color=\"black\", label='Analytical solution (present study)')\n",
    "plt.plot(y1,P_Y_1[:,300],linestyle='--',linewidth=2.5,color=\"black\")\n",
    "plt.plot(Gong_x_1M,Gong_y_1M,linestyle='-',marker='d',linewidth=1.5,color=\"m\", label='Field observation\\n(Chaosittichai and Anantanasakul, 2018)')\n",
    "plt.plot(Gong_x_2M,Gong_y_2M,linestyle='-',marker='d',linewidth=1.5,color=\"m\")\n",
    "plt.plot(API_y_1,API_P1_1,linestyle=':',linewidth=2.5,color=\"black\", label='API method')\n",
    "plt.plot(API_y_1,API_P1_2,linestyle=':',linewidth=2.5,color=\"black\")\n",
    "#pop_a = mpatches.Patch(color=\"blue\", label='API method') \n",
    "#pop_b = mpatches.Patch(color='black',label='Analytical solution (present study)') \n",
    "#pop_c = mpatches.Patch(color='cornflowerblue', label='Field observation\\n(Gong and Anantanasakul, 2018)') \n",
    "#plt.legend(handles=[pop_a,pop_b,pop_c],frameon=False,loc = \"upper left\",labelspacing = 1.15,)\n",
    "#plt.legend(['Analytical solution at 1 m (present study)','Analytical solution at 2 m (present study)','Field observation\\n(Gong and Anantanasakul, 2018)','Field observation\\n(Gong and Anantanasakul, 2018)'],frameon=False) \n",
    "plt.xlabel('Horizontal displacement (m)',color=\"black\")\n",
    "plt.ylabel(\"Lateral soil resistance force (kN/m)\",color=\"black\")\n",
    "plt.legend(loc='upper left', frameon=False)\n",
    "plt.text(0.065,65, 'depth = 2 m')\n",
    "plt.text(0.083,18, 'depth = 1 m')\n",
    "plt.text(0.065,265, 'depth = 2 m')\n",
    "plt.text(0.065,185, 'depth = 1 m')\n",
    "plt.ylim(0, 350)\n",
    "plt.xlim(0, 0.10)\n",
    "plt.rcParams[\"figure.figsize\"] = (8.5,5.5)\n",
    "plt.rcParams.update({'font.size': 15})\n",
    "plt.rc('font',family='Times New Roman')\n",
    "plt.savefig(\"Fig Validation 6a 1m 2m.svg\", format=\"svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "517f68d3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98086848",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
